The police investigating a shooting in the Flatbush section of Brooklyn on Monday. The authorities said Officer Miguel Gonzalez killed Dwayne Jeune after Mr. Jeune approached officers with a knife.CreditJohn Taggart for The New York Times

The New York City police officer who shot and killed an emotionally disturbed man this week in Brooklyn appeared to have followed department protocols during the fatal encounter, the police commissioner said on Thursday.

The officer, Miguel Gonzalez, killed Dwayne Jeune on Monday while responding to a 911 call from Mr. Jeune’s mother, Dulcina Juene, who said her son had stopped taking his medication and was acting erratically. The police said Officer Gonzalez, a four-year veteran, shot Mr. Jeune, 32, after he approached officers with a large carving knife, knocking one of them to the ground after a stun gun failed to subdue him.

Asked about the shooting in a news conference on Thursday, the police commissioner, James P. O’Neill, said he had seen nothing to indicate that Officer Gonzalez had violated any Police Department rules.

“As far as everything I can see right now, all protocols were followed,” he said. “This incident happened very quickly.”

The internal review of the shooting, by the department’s Force Investigation Division, is expected to take several months.

In October, Officer Gonzalez shot and wounded an emotionally disturbed man wielding a knife in Brooklyn after the man called 911. Commissioner O’Neill said this week that the review of that shooting had not been completed but that investigators believed it was within guidelines.

The shooting this week drew attention to the slow progress in the department’s efforts to provide more training for officers in dealing with people who are in the midst of mental health crises, some of the most unpredictable situations officers face.

In October, a Sgt. Hugh Barry fatally shot Deborah Danner, a 66-year-old woman with bipolar disorder, in her Bronx apartment. In that case, Commissioner O’Neill and Mayor Bill de Blasio publicly faulted Sergeant Barry for not following department protocols, and in May, he was indicted on a charge of murder.

The Police Department, which has lagged behind many other cities in training front-line officers to deal with people with mental illnesses, began its current effort in 2015. But neither Sergeant Barry nor Officer Gonzalez had received crisis intervention training. The department said more than 5,600 of the 36,000 uniformed police officers in the city had received the training so far, and Commissioner O’Neill said the department would eventually provide the training to its entire patrol force, which is expected to reach 23,000 members by 2019.

Commissioner O’Neill said Ms. Danner’s death had prompted the department to focus on providing crisis intervention training to lieutenants, sergeants and certain neighborhood-based officers, which is expected to be completed in 2018. The department has doubled the number of officers it trains each week to 105, he said.

Mr. Jeune, an immigrant from Guyana who had received United States citizenship in the last two years, was shot inside his family’s apartment in East Flatbush, where his mother opened the door for four officers responding to her 911 call on Monday.

The next day, his parents stood in front of their apartment building with community leaders who called for an independent investigation of the shooting and a task force to examine how the Police Department responds to emotionally disturbed people. Mr. Jeune’s father, Vibert, questioned why Officer Gonzalez had been sent to his home after his involvement in the shooting in October.

“That officer has done bad things before,” Vibert Jeune said, “and to send him back to calm a situation — oh, he didn’t calm a situation. He made it worse.”

A version of this article appears in print on , on Page A20 of the New York edition with the headline: Officer Acted Within Rules In Shooting, Police Say. Order Reprints | Today’s Paper | Subscribe